# Questions tagged [group-theory]

Groups are an abstract algebraic concept based on a set and a group law (a binary function which closes the set).

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### Is modulus a prime number important for non-symmetric cryptology?

From this link Generation of a cyclic group of prime order we know how to generate a prime order group. This illustrates why a prime order group is important. But why is modulus a prime number ...
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### Is that possible to calculate modular inverse of a point on elliptic curves?

Imagine that you are given a point $P$ so that $P=a\times G$. If you have no knowledge of $a$ is that possible to calculate point $I$ so that $I$ is the modular inverse of $P$? We know that over ...
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### Operation Table for Permutation Group

I cannot seem to figure out how the operation table for this permutation is formed. Is it multiplying each index and doing modulus? I can't seem to figure out. This is a Table 4.2 found in "...
May be a silly doubt, please rectify my confusion regarding below problem: For concreteness assume $g=2, p=11, a=6$ and $x=9$ $$A = g^a \bmod p = 2^6 \bmod 11 = 9$$ $$X = g^x \bmod p = 2^9 \bmod 11 ... 1answer 54 views ### Message mapping to elliptic curve in BLS signature In the BLS signature the subgroup G of elliptic curve constructed with point P with prime order q by G=\langle P\rangle . The h(x) is a hash function. The point S is map (image) of h(m) ... 1answer 53 views ### Research topics related to cryptography and Hamiltonian cycles I am very interested in pursuing a research where I can show an application of Hamiltonian cycles in Cayley graphs of some group such as reflection groups to the field of cryptography. But currently ... 1answer 51 views ### Discrete log problem exponential runtime I am trying to understand the runtime complexity of the discrete log problem (in the most basic sense). So, if we have \langle g \rangle = G and are trying to find g^x = a, a \in G, 0 < x < ... 1answer 159 views ### Order of subgroups formed by Elliptic Curves with a Cofactor In this question: Why are the lower 3 bits of curve25519/ed25519 secret keys cleared during creation? The answer indicates that the order of all points on the curve over the finite field ... 1answer 35 views ### Multiplying between generators degree I have to elements of multiplicative group of finite field with generator g -$$g^x,g^y $$Can I get?$$g^{xy} 
In the Lelantus Paper, the authors mentionned this: In our case, the commitment key ck specifies a prime-order group G and three orthogonal group generators $g, h_1$ and $h_2$. G is mentioned in ...